'Only comparable' T -transitive property and its closures for IVFRs

In this paper a weaker kind of transitive property for interval-valued fuzzy relations (IVFRs) is introduced. It is called ’only comparable’ T-transitivity because it relaxes the need that all intervals must be comparable, by just the need of having T-transitive cycles only for comparable intervals. This paper also defines a weak concept of closure, and it is proved that it exists just one T transitive and weak T -transitive closure, it does not exists an ’only comparable’ T -transitive weak closure, but there exist many ’only comparable’T transitive weak closures of anIVFR.

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